Question Number 154385 by amin96 last updated on 17/Sep/21 $${if}\:\:\:\sqrt[{\mathrm{3}}]{{x}}−\sqrt[{\mathrm{3}}]{{x}−\mathrm{36}}=\mathrm{3}\:\:\:\:\:\:{find}\:\:\:\:{x}−\frac{\mathrm{1}}{{x}} \\ $$ Answered by amin96 last updated on 18/Sep/21 $${x}={t}^{\mathrm{3}} \:\:\:\Rightarrow\:\:\:{t}−\sqrt[{\mathrm{3}}]{{t}^{\mathrm{3}} −\mathrm{36}}=\mathrm{3}\:\:\Rightarrow\:\:\sqrt[{\mathrm{3}}]{{t}^{\mathrm{3}} −\mathrm{36}}={t}−\mathrm{3} \\ $$$${t}^{\mathrm{3}}…
Question Number 154384 by mathdanisur last updated on 17/Sep/21 $$\mathrm{If}\:\:\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:\:\mathrm{then}: \\ $$$$\frac{\mathrm{4x}^{\mathrm{2}} }{\mathrm{x}+\mathrm{y}}\:+\:\frac{\mathrm{8y}^{\mathrm{2}} }{\mathrm{y}+\mathrm{z}}\:+\:\frac{\mathrm{4z}^{\mathrm{2}} }{\mathrm{z}+\mathrm{x}}\:\geqslant\:\mathrm{2x}\:+\:\mathrm{5y}\:+\:\mathrm{z} \\ $$ Answered by ghimisi last updated on 18/Sep/21 $$\mathrm{4}\left(\frac{{x}^{\mathrm{2}}…
Question Number 154380 by liberty last updated on 17/Sep/21 Answered by EDWIN88 last updated on 18/Sep/21 Commented by Tawa11 last updated on 21/Sep/21 $$\mathrm{Nice}\:\mathrm{sir} \\…
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Question Number 154372 by mathdanisur last updated on 17/Sep/21 $$\mathrm{If}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} =\mathrm{3} \\ $$$$\mathrm{Then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\Sigma\:\frac{\mathrm{a}^{\mathrm{3}} }{\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{b}\:+\:\mathrm{bc}}\:\geqslant\:\mathrm{1} \\ $$ Terms of Service Privacy…
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Question Number 88811 by jagoll last updated on 13/Apr/20 $$\begin{cases}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \left({y}+\mathrm{1}\right)^{\mathrm{2}} =\mathrm{27}{xy}}\\{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({y}^{\mathrm{2}} +\mathrm{1}\right)\:=\mathrm{10}{xy}}\end{cases} \\ $$ Answered by john santu last updated on 13/Apr/20 $${let}\:{me}\:{try}\:…
Question Number 154328 by liberty last updated on 17/Sep/21 $$\:{S}=\frac{\mathrm{1}}{\mathrm{1}+\mathrm{10}}+\frac{\mathrm{2}}{\mathrm{1}+\mathrm{10}^{\mathrm{2}} }+\frac{\mathrm{4}}{\mathrm{1}+\mathrm{10}^{\mathrm{4}} }+\frac{\mathrm{8}}{\mathrm{1}+\mathrm{10}^{\mathrm{8}} }+\ldots\: \\ $$$$ \\ $$ Answered by MJS_new last updated on 17/Sep/21 $$\mathrm{having}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{we}\:\mathrm{could}\:\mathrm{substract}\:\mathrm{the}…
Question Number 154320 by mathdanisur last updated on 17/Sep/21 $$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{ab}+\mathrm{bc}+\mathrm{ca}=\mathrm{2}\:\:\mathrm{then}: \\ $$$$\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\frac{\mathrm{a}\left(\mathrm{b}^{\mathrm{4}} \:+\:\mathrm{c}^{\mathrm{4}} \right)}{\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{2}} \mathrm{c}\:+\:\mathrm{bc}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{3}} }\:\geqslant\:\mathrm{1} \\ $$ Answered by ghimisi last…